Principles of Hindu Reckoning (Kitab fi usul hisab al-hind) is a mathematics book written by the 10th- and 11th-century Persian mathematician Kushyar ibn Labban. It is the second-oldest book extant in Arabic about Hindu arithmetic using Hindu-Arabic numerals ( ० ۱ ۲ ۳ ۴ ۵ ۶ ۷ ۸ ۹), preceded by Kibab al-Fusul fi al-Hisub al-Hindi by Abul al-Hassan Ahmad ibn Ibrahim al-Uglidis, written in 952. Although Al-Khwarzimi also wrote a book about Hindu arithmetic in 825, his Arabic original was lost, and only a 12th-century translation is extant. Kushyar ibn Labban did not mention the Indian sources for Hindu Reckoning, and there is no earlier Indian book extant which covers the same topics as discussed in this book. Principles of Hindu Reckoning was one of the foreign sources for Hindu Reckoning in the 10th and 11th century in India. It was translated into English by Martin Levey and Marvin Petruck in 1963 from the only extant Arabic manuscript at that time: Istanbul, Aya Sophya Library, MS 4857 and a Hebrew translation and commentary by Shālôm ben Joseph 'Anābī. Indian dust board Hindu arithmetic was conducted on a dust board similar to the Chinese counting board. A dust board is a flat surface with a layer of sand and lined with grids. Very much like the Chinese counting rod numerals, a blank on a sand board grid stood for zero, and zero sign was not necessary. Shifting of digits involves erasing and rewriting, unlike the counting board. Content There is only one Arabic copy extant, now kept in the Hagia Sophia Library in Istanbul. There is also a Hebrew translation with commentary, kept in the Bodleian Library of Oxford University. In 1965 University of Wisconsin Press published an English edition of this book translated by Martin Levey and Marvin Petruck, based on both the Arabic and Hebrew editions. This English translation included 31 plates of facsimile of original Arabic text. Principles of Hindu Reckoning consists of two parts dealing with arithmetics in two numerals system in India at his time. Part I mainly dealt with decimal algorithm of subtraction, multiplication, division, extraction of square root and cubic root in place value Hindu-numeral system. However, a section on "halving", was treated differently, i.e., with a hybrid of decimal and sexagesimal numeral. The similarity between decimal Hindu algorithm with Chinese algorithm in Sunzi Suanjing are striking, except the operation halving, as there